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arXiv:1105.2312 · Physical Review Letters

Quantum Spatial Superresolution by Optical Centroid Measurements

Heedeuk Shin, Kam Wai Clifford Chan, Hye Jeong Chang, Robert W. Boyd

Published Aug 19, 2011• 62 citations
arXivHTMLPDF

Abstract

Quantum lithography (QL) has been suggested as a means of achieving enhanced spatial resolution for optical imaging, but its realization has been held back by the low multiphoton detection rates of recording materials. Recently, an optical centroid measurement (OCM) procedure was proposed as a way to obtain spatial resolution enhancement identical to that of QL but with higher detection efficiency (M. Tsang, Phys. Rev. Lett. 102, 253601 (2009)). Here we describe a variation of the OCM method with still higher detection efficiency based on the use of photon-number-resolving detection. We also report laboratory results for two-photon interference. We compare these results with those of the standard QL method based on multiphoton detection and show that the new method leads to superresolution but with higher detection efficiency.

DOI
10.1103/physrevlett.107.083603

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Quantum lithography (QL) has been suggested as a means of achieving enhanced spatial resolution for optical imaging, but its realization has been held back by the low multiphoton detection rates of recording materials. Recently, an optical centroid measurement (OCM) procedure was proposed as a way to obtain spatial resolution enhancement identical to that of QL but with higher detection efficiency (M. Tsang, Phys. Rev. Lett. 102, 253601 (2009)). Here we describe a variation of the OCM method with still higher detection efficiency based on the use of photon-number-resolving detection. We also report laboratory results for two-photon interference. We compare these results with those of the standard QL method based on multiphoton detection and show that the new method leads to superresolution but with higher detection efficiency.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated NNN-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N1/N1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated N-photon state, the method of optical centroid measurement (OCM) was shown to exhibit a resolution enhancement by improving the classical Rayleigh limit by a factor of 1/N. In this work, the theory of OCM is formulated within the framework of an imaging formalism and is implemented in an exemplary experiment by means of a conventional entangled photon pair source. The expected resolution enhancement of a factor of two is demonstrated. The here presented experiment allows for single-shot operation without scanning or iteration to reproduce the object in the image plane. Thereby, photon detection is performed with a newly developed integrated time-resolving detector array. Multi-photon interference effects responsible for the observed resolution enhancement are discussed and possible alternative implementation possibilities for higher photon number are proposed.
The method of optical centroid measurement (OCM) has shown to exhibit spatial super-resolution with enhancements at the Heisenberg limit in plane wave interference experiments. In this work, the OCM method is for the first time used in an imaging setting where actual object features are observed. The OCM result is rederived in a near-field imaging formalism for a general imaging system and in full 2-D treatment. Analogies to coherent and incoherent imaging are shown Moreover, coherent OCM imaging is experimentally implemented for photon number N = 2, where an experimental setup is presented which allows to generate the desired entangled two-photon state containing the super-resolved image. This state is then imaged by an imaging system with a finite resolution defined by its point spread function (PSF). The centroid measurement of the two-photon states delivers then an image with a width of the PSF reduced by a factor 2 corresponding to the Heisenberg limit. In the experiment, the object is illuminated by a continuous-wave pump laser centred at 405nm with an output power of 30mW. A 4-f lens system images the object to the state preparation output plane. In the far-field plane between the lenses, a 5mm long periodically poled KTiOPO4 non-linear crystal generates photon pairs at 810nm by type-0, frequency-degenerate and collinear spontaneous parametric down-conversion. This generated OCM state is then imaged by a single lens and detected in coincidence by a fully digital 2-D sensor array with single-photon sensitivity and per-pixel sub-nanosecond time resolution. The OCM state is spectrally filtered at 810nm. Its imaging capability is compared to classical light sources including spatially coherent, monochromatic illumination at 405nm and 810 nm, as well as spatially incoherent light at 810 nm. The former is implemented using collimated lasers, the latter is a thermal light source spectrally filtered at 810 nm. The PSF of the different light sources are compared at low numerical aperture by imaging a focal point of 25μm Gaussian waist radius.